Finite Group Databasebeta

← C5×#23987 #11946707

Subgroups — C5×#23987 #11946707

Order 1280.

1514 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3490C211yesmaximal, characteristic, complemented
2C5×#2613C212yesmaximal, complemented
3C5×#2308C211yesmaximal, characteristic, complemented
4C5×#2030C211yesmaximal, characteristic, complemented
5C5×#2029C211yesmaximal, characteristic, complemented
6C5×#2022C211yesmaximal, characteristic, complemented
7C5×#2021C211yesmaximal, characteristic, complemented
8C5×#1898C212yesmaximal, complemented
9C5×#1890C212yesmaximal, complemented
10C5×#1889C212yesmaximal, complemented
11C5×#1819C211yesmaximal, characteristic, complemented
12C23×C5×D4C2211yescharacteristic
13C5×#551—24no—
14C5×#546—24no—
15C5×#543C2211yescharacteristic
16C5×#538—22no—
17C5×#534C2211yescharacteristic
18C5×#525—22no—
19C2×C5×#123C2212yes—
20C2×C5×#120C2212yes—
21C2×C5×#120C2212yes—
22C5×#518C2212yes—
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C2×C5×#99C2212yes—
26C2×C5×#99C2212yes—
27C5×#394—24no—
28C5×#392—24no—
29C5×#386—22no—
30C5×#386—22no—
31C5×#381C2211yescharacteristic
32C5×#381C2212yes—
33C5×#381C2211yescharacteristic
34C5×#379C2211yescharacteristic
35C5×#379C2212yes—
36C5×#379C2211yescharacteristic
37C5×#379C2212yes—
38C5×#342C2211yescharacteristic
39C5×#342C2211yescharacteristic
40C5×#342C2212yes—
41C5×#342C2212yes—
42C5×#342C2212yes—
43#23987C511yesmaximal, characteristic, direct product factor, Sylow
44C25×C5C2311yescharacteristic
45C25×C5C2311yescharacteristic
46C2×C5×#41—22no—
47C22×C5×D4—21no—
48C22×C5×D4—21no—
49C22×C5×D4—22no—
50C22×C5×D4—24no—
51C22×C5×D4—22no—
52C22×C5×D4—22no—
53C22×C5×D4—42no—
54C22×C5×D4D414yescomplemented
55C22×C5×D4C2312yes—
56C23×C4×C5—21no—
57C23×C4×C5D412yescomplemented
58C23×C4×C5C2311yescharacteristic
59C5×#126—24no—
60C5×#124—24no—
61C5×#123—24no—
62C5×#123—24no—
63C5×#123—22no—
64C5×#123—24no—
65C5×#123—42no—
66C5×C22⋊Q8—22no—
67C5×C22⋊Q8—22no—
68C5×C22⋊Q8—24no—
69C5×#121—22no—
70C5×#121—24no—
71C5×#121—22no—
72C5×#120—22no—
73C5×#120—22no—
74C5×#120—24no—
75C5×#120—22no—
76C5×#120—24no—
77C5×#120—42no—
78C4×C5×D4—24no—
79C4×C5×D4—24no—
80C4×C5×D4—24no—
81C5×#117—22no—
82C5×#117—22no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C22⋊C4—24no—
85C2×C5×C22⋊C4—22no—
86C2×C5×C22⋊C4—21no—
87C2×C5×C22⋊C4—22no—
88C2×C5×C22⋊C4—22no—
89C2×C5×C22⋊C4—24no—
90C2×C5×C22⋊C4—22no—
91C2×C5×C22⋊C4—22no—
92C2×C5×C22⋊C4—24no—
93C2×C5×C22⋊C4—42no—
94C2×C5×C22⋊C4D412yescomplemented
95C2×C5×C22⋊C4D414yescomplemented
96C2×C5×C22⋊C4C2312yes—
97C2×C5×C22⋊C4C2311yescharacteristic
98C2×C5×C22⋊C4C2311yescharacteristic
99C2×C5×C22⋊C4C2312yes—
100C2×C5×C22⋊C4C2311yescharacteristic
101C2×C5×C22⋊C4C2311yescharacteristic
102C2×C5×C22⋊C4C2312yes—
103C5×#99—42no—
104C5×#99—42no—
105C5×#95—22no—
106C5×#95—22no—
107C5×#95—24no—
108#3490C2×C511yescharacteristic, complemented
109#2613C2×C512yescomplemented
110#2308C2×C511yescharacteristic, complemented
111#2030C2×C511yescharacteristic, complemented
112#2029C2×C511yescharacteristic, complemented
113#2022C2×C511yescharacteristic, complemented
114#2021C2×C511yescharacteristic, complemented
115#1898C2×C512yescomplemented
116#1890C2×C512yescomplemented
117#1889C2×C512yescomplemented
118#1819C2×C511yescharacteristic, complemented
119C24×C5—21no—
120C24×C5—21no—
121C24×C5—22no—
122C24×C5—21no—
123C24×C5—22no—
124C24×C5—21no—
125C24×C5—22no—
126C24×C5—82no—
127C24×C5—82no—
128C24×C5C2×D412yes—
129C24×C5C2×D414yes—
130C24×C5C2×D411yescharacteristic
131C24×C5C2×D411yescharacteristic
132C24×C5#4112yescomplemented
133C24×C5C2411yescharacteristic
134C5×#41—84no—
135C2×C5×Q8—22no—
136C2×C5×D4—24no—
137C2×C5×D4—24no—
138C2×C5×D4—24no—
139C2×C5×D4—22no—
140C2×C5×D4—22no—
141C2×C5×D4—22no—
142C2×C5×D4—22no—
143C2×C5×D4—22no—
144C2×C5×D4—22no—
145C2×C5×D4—22no—
146C2×C5×D4—24no—
147C2×C5×D4—48no—
148C2×C5×D4—48no—
149C2×C5×D4—42no—
150C2×C5×D4—42no—
151C2×C5×D4—42no—
152C2×C5×D4—42no—
153C2×C5×D4—44no—
154C2×C5×D4—84no—
155C2×C5×D4—84no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5—24no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—22no—
167C22×C4×C5—42no—
168C22×C4×C5—82no—
169C22×C4×C5—82no—
170C22×C4×C5C2×D412yes—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D414yes—
173C22×C4×C5C2×D412yes—
174C22×C4×C5#4112yescomplemented
175C5×C4⋊C4—24no—
176C5×C4⋊C4—22no—
177C5×C4⋊C4—22no—
178C5×C4⋊C4—24no—
179C5×C4⋊C4—44no—
180C5×C22⋊C4—24no—
181C5×C22⋊C4—24no—
182C5×C22⋊C4—24no—
183C5×C22⋊C4—24no—
184C5×C22⋊C4—24no—
185C5×C22⋊C4—22no—
186C5×C22⋊C4—22no—
187C5×C22⋊C4—22no—
188C5×C22⋊C4—22no—
189C5×C22⋊C4—22no—
190C5×C22⋊C4—22no—
191C5×C22⋊C4—22no—
192C5×C22⋊C4—22no—
193C5×C22⋊C4—22no—
194C5×C22⋊C4—22no—
195C5×C22⋊C4—44no—
196C5×C22⋊C4—44no—
197C5×C22⋊C4—42no—
198C5×C22⋊C4—82no—
199C5×C22⋊C4—82no—
200C5×C22⋊C4—84no—
201C5×C22⋊C4—84no—
202C42×C5—24no—
203C23×D4C22×C511yescharacteristic
204#551—24no—
205#546—24no—
206#543C22×C511yescharacteristic
207#538—22no—
208#534C22×C511yescharacteristic
209#525—22no—
210C2×#123C22×C512yes—
211C2×#120C22×C512yes—
212C2×#120C22×C512yes—
213#518C22×C512yes—
214C22×C22⋊C4C22×C511yescharacteristic
215C22×C22⋊C4C22×C511yescharacteristic
216C2×#99C22×C512yes—
217C2×#99C22×C512yes—
218#394—24no—
219#392—24no—
220#386—22no—
221#386—22no—
222#381C22×C511yescharacteristic
223#381C22×C511yescharacteristic
224#381C22×C512yes—
225#379C22×C511yescharacteristic
226#379C22×C511yescharacteristic
227#379C22×C512yes—
228#379C22×C512yes—
229#342C22×C512yes—
230#342C22×C511yescharacteristic
231#342C22×C511yescharacteristic
232#342C22×C512yes—
233#342C22×C512yes—
234C23×C5—21no—
235C23×C5—21no—
236C23×C5—21no—
237C23×C5—21no—
238C23×C5—24no—
239C23×C5—24no—
240C23×C5—22no—
241C23×C5—22no—
242C23×C5—24no—
243C23×C5—22no—
244C23×C5—22no—
245C23×C5—42no—
246C23×C5—42no—
247C23×C5—42no—
248C23×C5—44no—
249C23×C5—44no—
250C23×C5—42no—
251C23×C5—42no—
252C23×C5—44no—
253C23×C5—44no—
254C23×C5—44no—
255C23×C5—41no—
256C23×C5—41no—
257C23×C5—42no—
258C23×C5—82no—
259C23×C5—82no—
260C23×C5—82no—
261C23×C5—82no—
262C23×C5—84no—
263C23×C5—84no—
264C23×C5#12012yes—
265C23×C5#12012yes—
266C23×C5C22×D411yescharacteristic
267C23×C5C22×D412yes—
268C23×C5C2×#4111yescharacteristic
269C23×C5C2×#4111yescharacteristic
270C23×C5H(5,𝔽2)12yes—
271C5×Q8—82no—
272C5×D4—48no—
273C5×D4—48no—
274C5×D4—48no—
275C5×D4—42no—
276C5×D4—42no—
277C5×D4—42no—
278C5×D4—42no—
279C5×D4—84no—
280C5×D4—82no—
281C5×D4—88no—
282C2×C4×C5—22no—
283C2×C4×C5—22no—
284C2×C4×C5—24no—
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—22no—
288C2×C4×C5—24no—
289C2×C4×C5—22no—
290C2×C4×C5—44no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—42no—
294C2×C4×C5—42no—
295C2×C4×C5—42no—
296C2×C4×C5—44no—
297C2×C4×C5—44no—
298C2×C4×C5—42no—
299C2×C4×C5—42no—
300C2×C4×C5—44no—
301C2×C4×C5—41no—
302C2×C4×C5—41no—
303C2×C4×C5—42no—
304C2×C4×C5—42no—
305C2×C4×C5—82no—
306C2×C4×C5—84no—
307C2×C4×C5—84no—
308C25C23×C511yescharacteristic
309C25C23×C511yescharacteristic
310C2×#41—22no—
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—22no—
314C22×D4—24no—
315C22×D4—22no—
316C22×D4—22no—
317C22×D4—42no—
318C22×D4C5×D414yescomplemented
319C22×D4C23×C512yes—
320C23×C4—21no—
321C23×C4C5×D412yescomplemented
322C23×C4C23×C511yescharacteristic
323#126—24no—
324#124—24no—
325#123—24no—
326#123—24no—
327#123—22no—
328#123—24no—
329#123—42no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—24no—
333#121—22no—
334#121—24no—
335#121—22no—
336#120—22no—
337#120—22no—
338#120—24no—
339#120—22no—
340#120—24no—
341#120—42no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—24no—
345#117—22no—
346#117—22no—
347C2×C4⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4C5×D412yescomplemented
359C2×C22⋊C4C5×D414yescomplemented
360C2×C22⋊C4C23×C511yescharacteristic
361C2×C22⋊C4C23×C511yescharacteristic
362C2×C22⋊C4C23×C512yes—
363C2×C22⋊C4C23×C512yes—
364C2×C22⋊C4C23×C511yescharacteristic
365C2×C22⋊C4C23×C511yescharacteristic
366C2×C22⋊C4C23×C512yes—
367#99—42no—
368#99—42no—
369#95—22no—
370#95—22no—
371#95—24no—
372C22×C5—22no—
373C22×C5—24no—
374C22×C5—22no—
375C22×C5—22no—
376C22×C5—22no—
377C22×C5—22no—
378C22×C5—24no—
379C22×C5—41no—
380C22×C5—41no—
381C22×C5—42no—
382C22×C5—42no—
383C22×C5—42no—
384C22×C5—42no—
385C22×C5—42no—
386C22×C5—44no—
387C22×C5—44no—
388C22×C5—42no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5—44no—
393C22×C5—84no—
394C22×C5—84no—
395C22×C5—82no—
396C22×C5—82no—
397C22×C5—82no—
398C22×C5—84no—
399C22×C5—82no—
400C22×C5C2×#12011yescharacteristic
401C22×C5#52511yescharacteristic
402C22×C5#53511yescharacteristic
403C22×C5#54612yes—
404C22×C5#54612yes—
405C4×C5—42no—
406C4×C5—42no—
407C4×C5—42no—
408C4×C5—42no—
409C4×C5—44no—
410C4×C5—82no—
411C4×C5—81no—
412C4×C5—81no—
413C4×C5—82no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—21no—
418C24—22no—
419C24—21no—
420C24—22no—
421C24—82no—
422C24—82no—
423C24C2×C5×D412yes—
424C24C2×C5×D414yes—
425C24C2×C5×D411yescharacteristic
426C24C2×C5×D411yescharacteristic
427C24C5×#4112yescomplemented
428C24C24×C511yescharacteristic
429#41—84no—
430C2×Q8—22no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—24no—
442C2×D4—48no—
443C2×D4—48no—
444C2×D4—42no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—44no—
449C2×D4—84no—
450C2×D4—84no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—42no—
463C22×C4—82no—
464C22×C4—82no—
465C22×C4C2×C5×D412yes—
466C22×C4C2×C5×D412yes—
467C22×C4C2×C5×D414yes—
468C22×C4C2×C5×D412yes—
469C22×C4C5×#4112yescomplemented
470C4⋊C4—24no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—24no—
474C4⋊C4—44no—
475C22⋊C4—24no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—44no—
491C22⋊C4—44no—
492C22⋊C4—42no—
493C22⋊C4—82no—
494C22⋊C4—82no—
495C22⋊C4—84no—
496C22⋊C4—84no—
497C42—24no—
498C2×C5—21no—
499C2×C5—22no—
500C2×C5—22no—
501C2×C5—21no—
502C2×C5—42no—
503C2×C5—42no—
504C2×C5—82no—
505C2×C5—82no—
506C2×C5#240411yescharacteristic
507C2×C5#302612yes—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—24no—
513C23—24no—
514C23—22no—
515C23—22no—
516C23—24no—
517C23—22no—
518C23—22no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—44no—
523C23—44no—
524C23—42no—
525C23—42no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—82no—
533C23—82no—
534C23—82no—
535C23—82no—
536C23—84no—
537C23—84no—
538C23C5×#12012yes—
539C23C5×#12012yes—
540C23C22×C5×D411yescharacteristic
541C23C22×C5×D412yes—
542C23C2×C5×#4111yescharacteristic
543C23C2×C5×#4111yescharacteristic
544C23C5×H(5,𝔽2)12yes—
545Q8—82no—
546D4—48no—
547D4—48no—
548D4—48no—
549D4—42no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—84no—
554D4—82no—
555D4—88no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—44no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—82no—
580C2×C4—84no—
581C2×C4—84no—
582C5#2398711yescharacteristic, direct product factor, Sylow
583C22—22no—
584C22—24no—
585C22—22no—
586C22—22no—
587C22—24no—
588C22—22no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—44no—
598C22—44no—
599C22—42no—
600C22—42no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22—84no—
605C22—84no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—84no—
610C22—82no—
611C22C2×C5×#12011yescharacteristic
612C22C5×#52511yescharacteristic
613C22C5×#53511yescharacteristic
614C22C5×#54612yes—
615C22C5×#54612yes—
616C4—42no—
617C4—42no—
618C4—44no—
619C4—42no—
620C4—42no—
621C4—81no—
622C4—81no—
623C4—82no—
624C4—82no—
625C2—21no—
626C2—22no—
627C2—22no—
628C2—21no—
629C2—42no—
630C2—42no—
631C2—82no—
632C2—82no—
633C2C5×#240411yescharacteristic
634C2C5×#302612yes—
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC24C24×C5
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5×#3490C2semidirect
2. C5×#2613C2semidirect
3. C5×#2308C2semidirect
4. C5×#2030C2semidirect
5. C5×#2029C2semidirect
6. C5×#2022C2semidirect
7. C5×#2021C2semidirect
8. C5×#1898C2semidirect
9. C5×#1890C2semidirect
10. C5×#1889C2semidirect
11. C5×#1819C2semidirect
43. #23987C5direct (N × H)
54. C22×C5×D4D4semidirect
57. C23×C4×C5D4semidirect
94. C2×C5×C22⋊C4D4semidirect
95. C2×C5×C22⋊C4D4semidirect
108. #3490C2×C5semidirect
109. #2613C2×C5semidirect
110. #2308C2×C5semidirect
111. #2030C2×C5semidirect
112. #2029C2×C5semidirect
113. #2022C2×C5semidirect
114. #2021C2×C5semidirect
115. #1898C2×C5semidirect
116. #1890C2×C5semidirect
117. #1889C2×C5semidirect
118. #1819C2×C5semidirect
132. C24×C5#41semidirect
174. C22×C4×C5#41semidirect
318. C22×D4C5×D4semidirect
321. C23×C4C5×D4semidirect
358. C2×C22⋊C4C5×D4semidirect
359. C2×C22⋊C4C5×D4semidirect
427. C24C5×#41semidirect
469. C22×C4C5×#41semidirect
582. C5#23987direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#34902
C5×#26132
C5×#23082
C5×#20302
C5×#20292
C5×#20222
C5×#20212
C5×#18982
C5×#18902
C5×#18892
C5×#18192
#239875